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McGraw Hill Integrated II, 2012 View details

5. Parts of Similar Triangles

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Exercise 42 Page 590

Write a proportion using the Triangle Proportionality Theorem.

x=4, y=10

Practice makes perfect

Let's analyze the given figure. We will start by finding x.

We can see that two segments are congruent, so we will solve the equation 12x+12 = 32x+8 to find x. Let's do it!

1/2x+12 = 3/2x+8

▼

Solve for x

SubEqn

LHS-8=RHS-8

1/2x+4=3/2x

SubEqn

LHS-1/2x=RHS-1/2x

4=3/2x-1/2x

SubFrac

Subtract fractions

4=2/2x

QuotOne

a/a=1

4=x

RearrangeEqn

Rearrange equation

x=4

Since we are given a triangle with a line that is parallel to one of its sides, we can use the Triangle Proportionality Theorem.

If a segment parallel to one of the sides of a triangle is drawn between the other sides, the segment divides the other two sides proportionally.

Let's write a proportion using the expressions for the lengths of the segments. 2y+4/3y-6 = 12x+12/32x+8 Since we know that the two segments on the right side are congruent, we know that the two segments on the left side are also congruent. Let's solve the equation 2y+4 = 3y-6 to find y.

2y+4 = 3y-6

▼

Solve for y

AddEqn

LHS+6=RHS+6

2y+10=3y

SubEqn

LHS-2y=RHS-2y

10=y

RearrangeEqn

Rearrange equation

y=10